For example, as disclosed in Japanese Unexamined Patent Publication (Kokai) No. 10-182881, it has been proposed to compound stable free radicals such as TEMPO (i.e., 2,2,6,6-tetramethyl-1-piperidinyloxy) into rubber to improve the physical properties of the rubber composition, in particular those such as processability, abrasion resistance. Further, Japanese Unexamined Patent Publication (Kokai) No. 8-239510 proposes to include a TEMPO derivative in a polymer to prevent polymer aging. However, no reference can be found relating to positively the generation of carbon radical or radicals in polymers such as rubbers so as to modify polymers using a compound(s) having a stable free radical or the radicals in the molecule thereof.